I don't have a favourite character. All reveal themselves in interesting ways

I put on the Homeland boxset, "From one Muslim to another". And the president of the United States was tickled by my message, but I did lose confidence a couple of weeks later and contacted his press secretary at the time to check he had got the joke. And I received word that he had. And I obviously haven't upset him too much, because he's now a huge Billions fan.

Well, I hope to play Henry VIII one more time, because I believe Hillary Mantel is writing the third instalment of Wolf Hall, and Thomas Cromwell's still got four years left to live. But when, I don't know. There will be a third series of Billions later this year.

We saw you in The Goat on Thursday afternoon (the one with the annoying interruption from an iPhone, which you handled brilliantly). It seemed a pretty gruelling part to play – how does it rate against other roles you’ve tackled?

The role is tiring to play because in different ways Martin is a tragic centre of a comic situation. And so I have to remain absolutely true to the heartbreak of hurting my wife, the grief of losing my lover, and the personal dislocation and the exhaustion of having a divided self, for two hours on stage. Having said that, it's one of the most fun and energising roles I've ever played, if that's not a contradiction.

It's not as tiring as Hamlet.

Damian Lewis and Sophie Okonedo in The Goat, Or Who Is Sylvia by Edward Albee at the Theatre Royal Haymarket, London. Photograph: Tristram Kenton/The Guardian

Saw you on the tube the other day. We both alighted at Leicester Square and for a few seconds I was tempted to say something, to complement you on your body of work. But decided against it. Are you often recognised in an irritating way by complete strangers who ask to take selfies, etc? Or do you manage to remain relatively anonymous?

I get asked to stop a lot and have a photo, and sometimes it's impossible to stop - usually because I'm running slightly late, and I have to get somewhere on time. And so when I stop I'm afraid really depends on my mood and my circumstances. I like to stop for people if I can. If you had stopped me and said something sincere and heartfelt that would have been a very pleasant chat to have had, so I'm sorry you didn't.

I absolutely love the scenes in Billlions with you and David Costabile (Wags). It looks less like acting and more like two good friends having fun. Is that the case or are you the best actor on the planet?

Getting into a role

The first time I got to see you act was in The Forsyte Saga. Your character Soames had so much depth; I hated him, but I also felt his desperation, anger, immense sadness and longing. His idiosyncrasies were just as important for me as the script.How did you get so much depth into this character and do you spend time developing idiosyncrasies for roles you play??

I think the important thing for any actor in any role you play is to elicit some empathy from the audience, not sympathy, but empathy - an understanding of why the character behaves the way he does, however malevolent he is. What drives the malevolence, the desperation, why he feels so compromised. And why would he feel so compromised. So getting an audience to understand that, I think puts them in an interesting moral position, which is what interests me as an actor. Every good script has an argument in it, and the characters represent different sides of the argument. So that's what I try to do - and that's very different from wanting to be liked. I think if you want to be liked as an actor, you'll never be interesting.

In terms of idiosyncrasies, there's a funny story behind the rigidity and stiffness to Soames. On the first day of filming in Manchester, my appendix ruptured and I was admitted to the Manchester General Hospital, where I remained for over a week and I couldn't come back to work for two weeks. When I did return to work, I found they'd shot some wide shots, and used a background artist dressed up in a tailcoat and top hat to walk up to Irene's mother's front door, and initially I was incensed that they would have done that. And then I grew so fascinated with this background artist's walk that I stole it for Soames, and so some of the idiosyncratic stiffness in Soames, and his inability to express himself, comes from that extra. So thank you!

Yes, often when I'm in America I use my American accent all weekend when I don't need to - I go to the grocery store and ask for eggplant and zucchini. I can go a whole day like that. It confuses people when I switch mid-conversation, which I've done.

Post your questions for Damian Lewis

Damian Lewis is best known for three titanic roles on television: Major Richard Winters in Steven Spielberg’s Band of Brothers, an imperious but paranoid Henry VIII in Wolf Hall and the radicalised PoW Nicholas Brody in Homeland, for which he won a Golden Globe and Emmy in 2012. He’s currently starring in the US drama Billions, opposite Paul Giamatti.

On film there are brilliant curios such as Keane and Our Kind of Traitor, and his stage career is also notable. Lewis cut his teeth with the Royal Shakespeare Company, playing opposite Keira Knightley in a production of The Misanthrope, and he is currently tackling Edward Albee’s The Goat, or Who Is Sylvia? alongside Sophie Okonedo. The Guardian’s Michael Billington gave the production five stars, saying Lewis “pushes his capacity for guilt-ridden secrecy to the limit”.

Lewis joins us to answer your questions in a live webchat from 2pm on Wednesday 19 April. Post them in the comments below, and he’ll take on as many as possible.